Theorems · Theorem · group theory
AddCommGroup.smul_top_eq_top_of_divisibleBy_int
∀ (A : Type u_1) [inst : AddCommGroup A] [DivisibleBy A ℤ] {n : ℤ}, n ≠ 0 → n • ⊤ = ⊤- Defined in
- Mathlib.GroupTheory.Divisible
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupDivisibleBy
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement · cited by 9,680
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.pointwiseMulActionstatement · cited by 24
- DistribMulAction.toAddMonoidEndproof · cited by 9
- DivisibleBystatement and proof · cited by 8
- DivisibleBy.divproof · cited by 6
- AddSubgroup.map_top_of_surjectiveproof · cited by 5
- DivisibleBy.div_cancelproof · cited by 4
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